The present invention relates to a heat-flow analyzing method which is used for a plant simulation, etc. in the design evaluation, operation training, etc. of a heat transporting system in a power plant and which is required to correctly evaluate the liquid surface in a container containing a gaseous phase under the liquid surface, and also concerns an apparatus for carrying out such an analysis.
Heat-flow simulations have been generally carried out in which, in order to predict and estimate the behaviors of a fluid flowing through heat-transporting equipment such as pipes and containers in a plant, the pipes and containers are divided into a plurality of volume elements that are referred to as nodes, and conservation equations relating to the mass, the energy and the amount of motion in each node are used so as to carry out analyses. In this case, the analyses are carried out assuming that the pressure, the temperature and the void fraction (the ratio of existence of the gaseous phase in a mixed state of a gaseous phase and a liquid phase) are uniform inside each node. The assumption that the inside of each node is maintained uniform is appropriate when a flow is exerted through the pipes and containers; however, when a liquid surface exists, the assumption is not appropriate since the void fraction drastically changes due to the rise and drop of the liquid surface. For example, in a case where the void fraction drops, if the drastic changes in the void fraction at the liquid surface is not taken into consideration, the void fraction in an upper node tends to start dropping before a lower node has been filled with the liquid, thereby failing to correctly simulate the behaviors of the liquid surface. For this reason, conventionally, models for taking the liquid surface into consideration are incorporated into various analysis codes. For example, in TRAC-BF1/MOD1 which is a typical heat-flow analysis code used in the gas-liquid two-phase flow analysis in the nuclear power plant, the following liquid-surface model is incorporated in accordance with the nuclear-plant designing standard NUREG/CR-4391 (1992). Supposing that there is no change in the flow-passage area, that the void fraction distribution shows a normal distribution in which the void fraction increases as the level becomes higher, and that as illustrated in FIG. 2, the node number reduces as the level becomes higher, when the void fraction a satisfies the following inequalities:
xcex1j+1 less than xcex1j less than xcex1jxe2x88x921, and 
(xcex1jxe2x88x921xe2x88x92xcex1j greater than 0.2 or xcex1jxe2x88x92xcex1j+1 greater than 0.2), and 
xcex1jxe2x88x921 greater than 0.7,
a judgement is made that the liquid surface is located at node j. Moreover, with respect to the node that is judged as having the liquid surface, supposing that the void fraction is represented by xcex1+ above the level and xcex1xe2x88x92 below the level, the discharge rate between the nodes is found. Here, xcex1+ and xcex1xe2x88x92 are values that satisfy 0xe2x89xa6xcex1xe2x88x92 less than xcex1j less than xcex1+xe2x89xa61.
In FIG. 11, reference numeral 1 represents an upper node in the case of no liquid surface model incorporated, reference numeral 2 represents a node that is originally supposed to have a liquid surface, reference numeral 3 represents a lower node, reference numeral 4 is a passage between 2 and 1, and reference numeral 5 represents a passage between 2 and 3. Moreover, reference numeral 7 represents an upper node in the case when a liquid surface model is incorporated, reference numeral 8 is a liquid surface node, reference numeral 9 represents a lower node, reference numeral 10 is a passage between 7 and 8, and reference numeral 11 is a passage between 8 and 9. Reference numeral 12 represents a liquid surface. An arrow on the junction 10 or 11 shows a flow direction which is taken to be positive in the calculation.
A conventional liquid-surface analyzing method and apparatus has a structure as described above, and there are many values which have been set based upon experience; therefore, in the case of a difference between the size of nodes and the tendency of the void distribution, it becomes difficult to make proper evaluation, and the analysis model needs to be adjusted every time it is set. Moreover, another disadvantage is that the range of conditions for correct operation of the liquid surface model is limited. In the conventional technique, it is mainly applied to an analysis model in which its range of use is limited as in the case of a numerical analysis, etc., and in most cases, the results of analysis are evaluated by experienced designers familiar with the analysis model; therefore, these problems are permissible. However, in the case of application to an analysis model used as a plant simulator, first, the range of use is not limited, and second, the users, who are operators, etc., in most cases, tend to be completely ignorant about the analysis model; therefore, the method has to make correct evaluation on the liquid surface in general in all cases.
More specifically, in the case when a liquid surface is formed in pipes and containers in a plant, there is a case in which a gaseous phase and a liquid phase are completely separated from each other above and below the liquid surface, or there is a case in which a large number of voids are included below the liquid surface as seen in a depressurized boiling state; therefore, a liquid-surface evaluation method which can evaluate. the liquid surface correctly in general in all operation conditions in a plant is demanded. Moreover, it is also necessary to take it into account the following point: in a pipe or a tank in which water below a saturation temperature and vapor are located with the liquid surface in between, since heat transfer between the gas and liquid is carried out only by the liquid surface, the temperature of the liquid phase is maintained at not more than the saturation temperature for a long time, while in the case when a large number of bubbles are located below the liquid surface as seen in a depressurized boiling state, since the gas-liquid interfacial area is represented by the sum of the bubble surfaces and liquid surface, the heat transfer between the gas and liquid takes place rapidly. Moreover, in the case when a liquid surface model is incorporated, in particular, if the liquid surface shifts in a manner bridging a node, a switchover is made from the liquid surface node to the normal node (the node which does not include the liquid surface); and at this time, it is necessary to avoid the analysis from becoming unstable due to drastic changes in the gas-liquid interfacial area.
The present invention has been devised in order to solve the above-mentioned problems with the conventional heat-flow analyzing method for two gaseous and liquid phases and the apparatus thereof, and its objective is to provide a heat-flow analyzing method for two gaseous and liquid phases which can evaluate the position of the liquid surface and its shift correctly whether or not bubbles exist below the liquid surface, and which can also evaluate the heat transfer between the two gaseous and liquid phases correctly, or an apparatus used in such a method.
In the two-phase heat-flow analyzing method related to the first arrangement of the present invention which is a method for analyzing the heat-transfer behaviors of a two-phase fluid flowing through heat-transport equipment, the heat-transport equipment is divided into a plurality of nodes, the void fraction of a gaseous phase above the liquid surface of a node possessing the liquid surface and the void fraction below the liquid surface thereof are calculated based upon the void fraction of the node in question and the void fraction of a node below the node in question, and based upon the results of the calculations, the position of a liquid surface inside the heat-transport equipment is calculated.
Moreover, in the two-phase heat-flow analyzing method related to the second arrangement of the present invention, based upon the void fractions of a target node to be judged and nodes located above and below the target node, a judgement is made as to whether or not the target node possesses a liquid surface.
Furthermore, in the two-phase heat-flow analyzing method related to the third arrangement of the present invention, based upon the respective void fractions of a target node to be judged and a node located below the target node, the void fraction of a gaseous phase above the liquid surface of the target node and the void fraction below the liquid surface are calculated, and based these void fractions, a judgement is made as to whether or not the target node possesses a liquid surface.
In the two-phase heat-flow analyzing method related to the fourth arrangement of the present invention, with respect to the node possessing a liquid surface, the quantity of heat transfer between the two gas-liquid phases is calculated based upon the void fraction of a gaseous phase above the liquid surface and the void fraction below the liquid surface.
Moreover, in the two-phase heat-flow analyzing apparatus of the fifth arrangement of the present invention which is an apparatus for analyzing the heat-transfer behaviors of a two-phase fluid flowing through heat-transport equipment, the heat-transport equipment is divided into a plurality of nodes, the void fraction of a gaseous phase above the liquid surface of a node possessing the liquid surface and the void fraction below the liquid surface thereof are calculated based upon the void fraction of the node in question and the void fraction of a node below the node in question, and based upon the results of the calculations, the position of a liquid surface inside the heat-transport equipment is calculated.
Moreover, in the two-phase heat-flow analyzing apparatus related to the sixth arrangement of the present invention, based upon the void fractions of a target node to be judged and nodes located above and below the target node, a judgement is made as to whether or not the target node possesses a liquid surface.
Furthermore, in the two-phase heat-flow analyzing apparatus related to the seventh arrangement of the present invention, based upon the respective void fractions of a target node to be judged and a node located below the target node, the void fraction of a gaseous phase above the liquid surface of the target node and the void fraction below the liquid surface are calculated, and based upon these void fractions, a judgement is made as to whether or not the target node possesses a liquid surface.
In the two-phase heat-flow analyzing apparatus related to the eighth arrangement of the present invention, with respect to the node possessing a liquid surface, the quantity of heat transfer between the two gas-liquid phases is calculated based upon the void fraction of a gaseous phase above the liquid surface and the void fraction below the liquid surface.
Referring to Figures, the following description will discuss embodiments of the present invention in detail.